Application of Sensitivity Analysis to the Finite Element Method

Finite element analysis and sensitivity analysis has §been performed on Poisson''s equation. An application §is that of potential flow, in which case Poisson s §equation reduces to Laplace s equation. The §stiffness matrix and its sensitivity are §evaluated by direct integration, as opposed to §numerical integration. This allows less §computational effort and minimizes the sources of §computational errors. The capability of evaluating §sensitivity derivatives has been added in order to §perform design sensitivity analysis of non-lifting §airfoils. The discrete-direct approach to §sensitivity analysis is utilized in the current §work. The potential flow equations and the §sensitivity equations are computed by using a §preconditioned conjugate gradient method which §greatly reduces the time required to perform §analysis, and the subsequent design optimization.§Airfoil shape is updated at each design iteration by §using a Bezier-Berstein surface parameterization. §The unstrucured grid is adapted considering the mesh §as a system of inteconnected springs. Numerical §solutions are compared with analytical results §obtained for a Joukowsky airfoil.